A dynamical implementation of colour coherence for quenched jets in JEWEL

This paper presents a dynamical implementation of colour coherence in the JEWEL event generator, where medium interactions are checked for their ability to resolve colour dipoles, leading to the disruption of angular ordering, a suppression of hard radiation, and observable modifications to jet properties such as the nuclear modification factor and fragmentation functions.

The Gist

Imagine you are watching a high-speed game of billiards, but instead of a table, the playing field is a super-hot, dense soup of energy created when heavy atoms smash into each other. This "soup" is called a quark-gluon plasma, and it's what scientists study to understand how the universe looked just after the Big Bang.

In this game, a "hard parton" (a tiny, high-energy particle) is shot through the soup. As it flies, it crashes into the particles in the soup, losing energy and creating a spray of new particles. This spray is what we call a jet.

For a long time, scientists had a simplified way of thinking about these crashes: they assumed every time the jet hit something in the soup, it was like hitting a single, isolated marble. But this paper introduces a more sophisticated rule called Colour Coherence.

Here is the story of what this paper does, explained simply:

1. The "Twin" Analogy: When Particles Act as One

In the quantum world, particles often come in pairs (or "dipoles") that are linked by an invisible force called "colour charge." Think of these two particles as twin siblings holding hands.

• The Old View: If a third person (a particle from the soup) bumps into the twins, the old models assumed the twins would react individually. One might get pushed left, the other right.
• The New View (Colour Coherence): The paper argues that if the bump is gentle (low energy), the twins are still holding hands so tightly that they react as one single unit. The bump doesn't have enough force to separate them or see them as two distinct people. They move together.
• The Resolution: However, if the bump is hard (high energy), it's like a strong shove that breaks their grip. Now the twins are separated, and they react individually.

The key discovery in this paper is that the "strength" of the shove determines whether the twins stay together or split up.

2. The "Dance Floor" and the "Bouncer"

Imagine the jet is a dancer trying to move through a crowded dance floor (the soup).

• Angular Ordering: In a normal dance (in a vacuum), a dancer has a specific rhythm. They can't spin wildly in every direction; their moves are "ordered." They spin within a certain cone.
• The Soup Effect: When the dancer enters the crowded soup, the crowd tries to stop them.
  • If the dancer is holding hands with a partner (the colour dipole) and the crowd gives a gentle nudge, the dancer and partner stay in sync. They keep their "ordered" dance rhythm.
  • If the crowd gives a hard shove that breaks their grip, the dancer loses their rhythm. They start flailing, spinning wildly, and making more random moves.

3. What Happens When We Fix the Rules?

The author, Korinna Zapp, updated a computer program called JEWEL (which simulates these collisions) to include this "holding hands" rule.

Here is what happened when the simulation ran with the new rules:

• Fewer Crashes: Because the twins often stay together and act as one big, smooth object, the crowd (the soup) doesn't "see" them as two separate targets to hit. It's harder to hit one big, smooth object than two small, jittery ones.
• Less Chaos: Since the twins stay together longer, they don't break apart as often. This means they don't start flailing (radiating energy) as much.
• Harder Jets: The result is that the jets coming out of the soup are "harder" and more focused. They lose less energy than the old models predicted. It's like a runner in a crowd who, by holding hands with a friend, manages to slip through the crowd more easily than if they were running alone and getting bumped constantly.

4. Why Does This Matter?

Scientists measure how much energy jets lose in these collisions to understand the properties of the "soup."

• The Problem: Previous models often predicted that jets would lose too much energy compared to what experiments actually see.
• The Solution: By adding the "Colour Coherence" rule (the twins holding hands), the simulation predicts that jets lose less energy. This brings the computer simulation much closer to the real data collected by giant detectors like ATLAS and CMS at the Large Hadron Collider.

The Bottom Line

This paper is like realizing that in a crowded room, people who are holding hands move differently than people walking alone. By teaching the computer to understand that these quantum particles sometimes act as a single team rather than individuals, the scientists can finally make their simulations match the real world.

It turns out that in the chaotic, hot soup of the early universe, sticking together is the best way to survive the crowd.

Technical Summary

1. Problem Statement

In high-energy heavy-ion collisions, hard partons traverse a dense, colored medium (Quark-Gluon Plasma), leading to jet quenching. A fundamental aspect of Quantum Chromodynamics (QCD) is colour coherence, where partons carrying matching color and anti-color charges interfere.

• In Vacuum: This leads to angular ordering, where subsequent gluon emissions are restricted to angles smaller than the opening angle of the parent dipole.
• In Medium: The medium acts as a "resolving" probe. If the transverse momentum transfer ($q_\perp$) of a scattering is sufficient to resolve the transverse separation ($d_\perp$) between the two legs of a color dipole, the coherence is broken, and the partons radiate independently. If $q_\perp$ is too small to resolve the separation, the dipole remains coherent and scatters/radiates as a single object.

Prior to this work, Monte Carlo models for jet quenching (like the Hybrid Model or JetMed) treated color coherence with fixed resolution scales or simplified assumptions. There was a lack of a fully dynamical implementation where the resolution of the medium is determined event-by-event based on the specific momentum transfer of individual scattering processes.

2. Methodology

The author implements a dynamical color coherence mechanism in the JEWEL (Jet Evolution With Energy Loss) event generator, version 2.6. JEWEL simulates jet evolution by interleaving vacuum-like parton showers with individual elastic and inelastic scatterings between hard partons and thermal medium constituents.

Key Implementation Steps:

1. Dipole Formation: When a parton splits ($a \to b + c$), a color dipole is formed between the daughter partons.
2. Scattering Check: For every potential re-scattering of a parton within a dipole, the code checks the transverse momentum transfer ($q_\perp$).
   • Resolved Scattering: If $q_\perp > 1/d_\perp$ (where $d_\perp$ is the transverse separation), the scattering is "resolved." The color coherence is broken; the parton is treated as an individual object, and angular ordering is disabled for its subsequent splittings.
   • Unresolved (Coherent) Scattering: If $q_\perp < 1/d_\perp$, the scattering is "unresolved." The dipole is treated as a single coherent object.
3. Coherent Evolution: To simulate coherent scattering, the algorithm temporarily "undoes" the splitting, treating the two daughter partons as a single effective parent parton. This effective parton undergoes elastic scattering. The deflections are then passed to the daughters upon "re-splitting."
   • Constraint: In this implementation, coherent scatterings are restricted to be elastic only (no induced radiation from coherent dipoles), and coherent states are limited to two partons.
4. Dynamic Angular Ordering: The implementation introduces a "Kinematics First" option for angular ordering.
   • If a parton (or its color partner) experiences a resolved scattering before the next splitting, angular ordering is turned off for that subsequent splitting.
   • If no resolved scattering occurs, angular ordering is enforced.
   • This allows the model to dynamically switch between coherent (angular ordered) and incoherent (no angular ordering) regimes based on the interaction history.

3. Key Contributions

• First Dynamical Implementation in JEWEL: Unlike previous models that used fixed resolution scales, JEWEL now determines the resolution scale dynamically for every interaction based on the momentum transfer.
• Restoration of Angular Ordering: The model demonstrates that color coherence effectively restores angular ordering for vacuum-like emissions in the medium, provided the partons have not been resolved by the medium.
• Decoupling of Scattering and Splitting: The work clarifies that while the number of scatterings per parton remains relatively constant (as unresolved scatterings are replaced by coherent ones), the radiation pattern changes drastically because coherent scatterings do not induce the same splitting cascades as resolved ones.
• Comparison of Angular Ordering Schemes: The paper introduces and benchmarks different strategies for imposing angular ordering constraints relative to kinematic constraints, finding that enforcing kinematics first yields better agreement with experimental data.

4. Results

The study compares JEWEL 2.6 results with and without the new color coherence implementation against experimental data from ATLAS and CMS at $\sqrt{s_{NN}} = 5.02$ TeV (Pb+Pb collisions).

• Nuclear Modification Factor ($R_{AA}$):

  • Implementing color coherence leads to a significant increase in $R_{AA}$ (less suppression).
  • This is counter-intuitive to some expectations but explained by the suppression of splittings. When coherence is maintained, angular ordering restricts the phase space for radiation, leading to fewer partons. Fewer partons mean fewer total scatterings with the medium, resulting in less overall energy loss.
  • The effect is so strong that turning on color coherence yields an $R_{AA}$ similar to a scenario without coherence where the scattering cross-section is artificially halved.

• Jet Fragmentation Functions:

  • Color coherence leads to a harder fragmentation pattern.
  • The suppression of splittings reduces the number of soft particles inside the jet.
  • The model with color coherence shows better agreement with ATLAS data compared to the version without coherence, particularly in the intermediate and hard momentum regions.

• Jet-Hadron Correlations:

  • Coherence reduces the number of particles at large angles ($\Delta R$) from the jet axis and suppresses the medium response component (soft particles generated by the medium).
  • The results with coherence align better with CMS data, specifically reducing the tension seen in the "kinematics only" (no coherence) scenarios which overproduce particles at intermediate angles.

• Vacuum vs. Medium:

  • In vacuum ($p+p$), the "Kinematics First" angular ordering option provides the best description of jet fragmentation and event shape data.
  • In the medium, the dynamical switching of angular ordering is crucial. The "Angular Ordering First" option (which forces ordering regardless of scattering) leads to overly soft fragmentation and poor agreement with data.

5. Significance

• Theoretical Insight: The paper confirms that the "resolution scale" of the medium is not a static parameter but a dynamic property emerging from the interplay between dipole size and momentum transfer.
• Phenomenological Impact: It highlights that angular ordering is a dominant mechanism in jet quenching. The suppression of radiation due to restored angular ordering (when coherence is maintained) is a more significant effect on jet quenching observables than the details of the scattering cross-section itself.
• Model Validation: The results suggest that experimental data (specifically jet fragmentation and sub-structure) favors models with a finite, dynamic resolution scale and coherent evolution, supporting the physical picture of antenna radiation in a medium.
• Future Directions: The implementation sets a new standard for Monte Carlo generators, emphasizing the need to treat vacuum-like and medium-induced emissions on equal footing regarding coherence, and suggests that future models must account for the fluctuations in momentum transfer that determine whether a dipole is resolved.

In summary, this work provides a rigorous, dynamical framework for color coherence in jet quenching, demonstrating that the interplay between medium resolution and angular ordering fundamentally alters the jet energy loss mechanism, leading to a harder fragmentation pattern and reduced overall suppression that aligns well with LHC data.